Field of the Invention
The invention concerns a method and device for determining at least one sample point specific vertical total electronic content.
The electromagnetic radio waves of all satellite based communications and/or navigation systems are subject to the interaction with the plasma of the ionosphere. The interaction is dispersive, i.e. strongly frequency dependent (proportional to 1/f2) and practically insignificant at oscillation frequencies f of more than 10 GHz. In the L-Band range used by the GNSS (Global Navigation Satellite Systems), the ionospheric propagation effects cannot be neglected. Therefore, knowledge of the current state of the ionosphere and resorting to error compensation measures are important.
Measurements of the code phase and the carrier phase are the basis of position determination with GNSS. The measured phase is determined by the phase-length ∫nds, where n is the ionospheric refractive index and s is referred to as the path length (or propagation path) element. In the geometric optics the propagation of the radio waves is further determined from Fermat's principle (the principle of the shortest arrival time), so that the propagation path with the minimum phase-length is to be found. For a refractive index n not equal to 1 this results in a lengthened beam path or transition time error compared to the comparison case of propagation of the wave in a vacuum. Ultimately in a GNSS the effect of the error is such that it causes errors in the distance between the satellites and the receiver determined by the receiver of the signals. In particular, a curvature of the beam path and an interaction of the wave with the medium that the wave passes through come under consideration as error sources. The invention is not limited to GNSS, however.
A complex nonlinear relationship of various geophysical parameters, for example ionization state, magnetic field state, and geometric parameters, for example elevation and/or azimuth, is used for the refractive index. The first approximation of the refractive index causes distance errors of the order of magnitude of up to about 100 m, which can be eliminated in GNSS by means of dual-frequency measurements. The corresponding methods are known. The higher order errors in the refractive index (˜1/fm, m>2) are of the order of magnitude of up to several centimeters.
It has already been proposed to correct first order errors (m=2) and errors caused by the curved propagation path by measurement and analysis of signals that have been received at different carrier frequencies (oscillation frequencies).
If only a single frequency receiver is provided, then no simple and accurate error correction is possible. In a single frequency measurement, a code phase can be represented in simplified form byΦ=ro+di+de  Formula 1where Φ denotes the code phase, ro denotes the distance between the transmitter and receiver, di denotes the ionospheric propagation error along the beam path and de denotes the remaining distance errors, such as for example clock errors.
The ionospheric propagation error can be more than 100 m, depending on the degree of ionization of the ionosphere. A suitable correction is therefore desirable, in particular in the area of space travel.
It is also known to perform an ionosphere correction depending on so-called vertical ionosphere errors, wherein to a first approximation the ionosphere error is proportional to a vertical total ionization of the ionosphere in relation to a surface area. The vertical total ionization or the vertical total electronic content is often also referred to as the TEC (total electron content). The vertical ionosphere error is used here as a reference for the calculation of an error along an arbitrarily oriented beam path described by an elevation angle and an azimuth. However, the real ionosphere is generally highly simplified for this. For example, in the absence of further information, it is assumed that the ionization is concentrated in a thin layer (thin shell model). A suitable transformation or mapping function will be referred to below as Thin-Shell-MF. One such Thin-Shell-MF is for example described in Jakowski et. al., “Relationship between GPS-signal propagation errors and EISCAT observations”, Ann. Geophysicae 14, pp. 1429-1436, Springer Verlag, 1996. An ionosphere altitude of 350 km is also described therein.
The simplifying assumption is made inter alia because in practice a distribution of the electron density along a beam path from the transmitter to the receiver is unknown. With the aforementioned thin shell model, it is assumed that the ionosphere is concentrated in a thin layer at an altitude of about 350 km to 400 km. By means of a geometric mapping function and with the adoption of the thin shell model, a defined vertical total electronic content at the point of intersection of the beam path with the thin ionosphere layer is converted into an electron content along the beam path.
Here, however, the usually varying electron density along the beam path is disadvantageously neglected. Likewise, vertical and horizontal gradients of the ionization are not taken into account. This can result in uncorrected residual errors of more than 10 m.
Vertical total electron contents for different latitudes and longitudes can be summarized in so-called TEC correction maps. If the thin shell model is used to produce said TEC correction maps, then there are already systematic errors during the generation of the correction maps, which can be propagated further and increased during the reverse transformation. In augmentation systems such as WAAS and EGNOS, the errors may not exceed predetermined threshold values according to the high safety standards that are usual in space travel. Both a very accurate calculation of the vertical TEC correction maps and also a best possible use of said maps for the error correction of the inclined beam paths are thus desired.
The subsequently published DE 10 2013 208 040.9 discloses a method and a device for determining an error during the propagation of an electromagnetic wave in an atmosphere comprising electrically charged particles. In the document it is described that an electron content along a beam path from the transmitter to the receiver can be calculated as the sum of electron contents of a plurality of increments or segments of the beam path. The electron contents of the increments are in turn determined depending on a vertical electron density distribution. Said vertical electron density distribution is in turn given by an analytically integratable physically realistic model of the vertical electron density distribution in the ionosphere, the integral of which corresponds to the predetermined vertical electron content. The formula for the Chapman layer that can be derived from the Chapman theory gives a realistic description of the vertical electron density distribution for example.
The book K. Davies, “Ionospheric Radio”, Peter Peregrinus Ltd, London, ISBN 086341186X, pages (60-65, 138), 1990 provides a realistic description of a vertical electron density distribution in the ionosphere.
The publication M. M. Hogue, “Higher order propagation effects and their corrections in precise GNSS positioning”, Siegen University Dissertation, DLR Research Report 2009-09, ISSN 1434-8454, 2009, Pages 218-224 describes an analytical solution of an integral over an electron density distribution.
This raises the technical problem of providing a method and device for the accurate determination of at least one sample point specific vertical total electronic content, wherein the vertical total electron contents determined in this way can then be used for more accurate determination of a propagation error or the improved determination of a residual error of an electromagnetic wave in an atmosphere, and hence also for more accurate position determination.